Primarily nonlinear effects observed in a driven asymmetrical vibrating wire

Abstract

The purpose of the work reported here is to further experimentally explore the wide variety of behaviors exhibited by driven vibrating wires, primarily in the nonlinear regime. When the wire is driven near a resonant frequency, it is found that most such behaviors are significantly affected by the splitting of the resonant frequency and by the existence of a "characteristic" axis associated with each split frequency. It is shown that frequency splitting decreases with increasing wire tension and can be altered by twisting. Two methods are described for determining the orientation of characteristic axes. Evidence is provided, with a possible explanation, that each axis has the same orientation everywhere along the wire. Frequency response data exhibiting nonlinear generation of transverse motion perpendicular to the driving direction, hysteresis, linear generation of perpendicular motion (sometimes tubular), and generation of motion at harmonics of the driving frequency are exhibited and discussed. Also reported under seemingly unchanging conditions are abrupt large changes in the harmonic content of the motion that sometimes involve large subharmonics and harmonics thereof. Slow transitions from one stable state of vibration to another and quasiperiodic motions are also exhibited. Possible musical significance is discussed.

Controllable damping of high- Q violin modes in fused silica suspension fibers

“…Since very small amplitudes of fiber vibrations occur in the test mass suspension, the simplest classical linear theory of a vibrating string is used for description of the fiber motion. Nonlinear effects are usually observed in strings vibrating with sufficiently large amplitudes [11]. It is known that each violin mode of the fiber corresponds to a harmonic oscillator.…”

A low-cost high-precision measurement method of string motion

“…Another optical method, less intrusive, expensive and cumbersome, consists in catching the shadow of the string by using an integrated opto-sensor [13], a photo-Darlington [14], or an analog position sensing detector [15], as well as an optoswitch system including an infrared emitting diode coupled to a photo-transistor [16]. The latter system has been used to measure the transverse [17,18] and longitudinal [19,20] string vibrations to analyse, for instance, nonlinear free vibrations [21] as well as chaotic vibrations [22] of a string. This system/sensor seems to be appropriate to measure the string displacement regardless of its material.…”